Modulator using the linear electro-optic effect of liquid crystals

ABSTRACT

This invention provides an electro-optic modulator which, in some embodiments, utilizes the linear electro-optic effect in liquid crystal materials. The liquid crystal modulator of this invention comprises a chiral smectic liquid crystal cell with electrodes to supply an electric field in a direction with a nonzero linear electro-optic coefficient, and means to suppress change in the tilt angle and azimuthal angle of the liquid crystal molecular directors. The response time of the linear electro-optic effect modulators of this invention is in the nanosecond range or faster. This modulator can be employed in Fabry-Perot or waveguide devices to provide increased modulation via multiple passes. This invention further provides for prism-coupling of light into or out of the waveguide structure whereby the modulator provides amplitude modulation, tunable filtering, or both. The prism-coupled waveguide filter is further provided for any electro-optic material, not limited to liquid crystals, and any electro-optic modulation mechanism, not limited to the linear electro-optic effect.

FIELD OF THE INVENTION

This invention relates to linear electro-optic modulation in liquidcrystal devices, in particular Fabry-Perot and prism-coupled waveguidedevices, and to electro-optically tunable prism-coupled waveguidefilters.

BACKGROUND OF THE INVENTION

There are several research territories which contribute to the prior artof the present invention. They include liquid crystal electro-opticmodulation, the dielectric properties of liquid crystals, second-ordernonlinear optical effects, and prism-coupled waveguides. Each isdiscussed below.

Liquid crystal electro-optic modulation has been utilized in a number ofdevice applications. Nematic liquid crystals provide analog retardationchanges due to rotation of birefringent molecules out of the plane ofthe incident optical field with tuning speeds of 1-100 ms. Chiralsmectic liquid crystals (CSLCs) provide tuning speeds of 1 μs. Whenincorporated in a "bookshelf" geometry cell (smectic layers orientedperpendicular to the substrate walls), analog CSLC materials, such asSmA* (S. T. Lagerwall et al. in U.S. Pat. No. 4,838,663) and distortedhelix ferroelectrics, DHF (L. A. Beresnev et al., European PatentApplication No. 309774, published 1989), display an analog tilt of thecell optical axis in the plane of the cell walls upon application of anelectric field across the smectic layers. In a discrete, multi-statecell, for example using ferroelectric SmC* or SmH* (N. A. Clark et al.in U.S. Pat. No. 4,367,924 and U.S. Pat. No. 4,563,059) orantiferroelectric phases (see for example, I. Nishiyama et al., Jpn. J.Appl. Phys. 28, L2248 (1989)), application of an electric field above acertain threshold voltage results in switching of the tilt of the CSLCmolecules between discrete stable states. In homeotropically alignedcells (smectic layers parallel to substrate walls) the optical axis ofthe CSLC material rotates in a plane perpendicular to the cell walls onapplication of an electric field across the smectic layers by electrodesthat are lateral to the substrate walls (Sharp et al., U.S. patentapplication 07/792,284 filed Nov. 14, 1991 and S. Garoff et al. Phys.Rev. Lett. 38, 848 (1977)). The devices of the prior art of nematicliquid crystal cell and CSLCs all function by large molecularreorientation of the molecular director (a vector on the long molecularaxis).

The dielectric properties of liquid crystals have been characterized bya number of groups (L. Bata et al., in Advances in Liquid CrystalResearch and Applications, edited by L. Bata, Pergamon Press (Oxford)1980, p. 251; A. Buka, ibid. p. 261; N. Maruyama, Ferroelectrics 58, 187(1984); and F. Gouda et al., Ferroelectrics 113, 165 (1991)). The modesutilized in the prior art of liquid crystal devices, which areassociated with reorientation of the molecular director, are identifiedin CSLCs as the Goldstone mode (azimuthal fluctuation of the moleculardirector) and the "soft" mode (fluctuation of the tilt angle). Typicalfrequencies for these modes are 10-100 Hz and 10⁴ -10⁵ Hz respectively.Both modes are present in SmC* materials and only the soft mode ispresent in SmA* materials. Other contributions to the dielectricpermittivity are identified as rotation about the molecular short axis,reorientation about the short-axis, rotation about the long axis, andintramolecular rotation about a single bond. These modes occur at higherfrequencies (10⁶ -10¹² Hz) than the molecular reorientation modes. Atstill higher frequency is electronic oscillation.

Optical second-order nonlinear (X²) effects include second harmonicgeneration (SHG), the linear electro-optic (EO) effect (Pockels effect),parametric amplification, optical rectification, and frequency mixing(see, for example, A. Yariv, Optical Electronics 3rd ed., CBS CollegePublisher, 1985). The origin of these nonlinear processes isfield-induced displacement of the centers of positive and negativecharged matter. In the linear EO effect, an applied electric fieldalters the index of refraction of the medium. This affords a convenientand widely used means of modulating the phase or intensity of opticalradiation. Applications of the linear EO effect include opticalmodulation, spectral filters, and beam deflectors.

In the prior art, second-order nonlinear optical effects have beendemonstrated in inorganic crystals and in organic materials such asLangmuir-Blodgett films, polymeric solid solutions, main chain polymers,and side chain polymers (T. Kondo et al., Jpn. J. Appl. Phys. 28, 1622(1989) and D. Jungbaver et al., J. Appl. Phys. 69, 8011 (1991)). Chiralsmectic liquid crystals in the thermodynamically stable smectic C* phasehave C₂ polar symmetry and possess macroscopic order, the requirementsfor displaying nonlinear optical effects. The inventors have previouslydemonstrated second harmonic generation with CSLCs (J. Y. Liu et al.,Opt. Lett. 15, 267 (1990) and J. Y. Liu, Ph.D. Thesis, University ofColorado, 1992). In addition, discovering the molecular criteria forCSLCs with increased nonlinear optical response and synthesizing suchcompounds has been undertaken (D. M. Walba et al., Mol. Cryst. Liq.Cryst. 198, 51 (1991) and J. Am. Chem Soc. 113, 5471 (1991)).

A technique is presented in the prior art for sensitive measurements ofdielectric materials using prism-coupled thin-film waveguides (P. K.Tien et al., J. Opt. Soc. Am. 60, 1325 (1970) and R. Ulrich et al.,Appl. Opt. 12, 2901 (1973)). Prism-coupling provides an efficient methodof coupling a light beam into a thin film waveguide. In this technique ahigh refractive index prism is placed above a thin-film waveguide,separated by a low index cladding layer. For efficient coupling, thecomponents of the wave vectors parallel to the gap are equal in theprism and the waveguide. This device has been demonstrated withinorganic thin-films.

Waveguides have been constructed with both nematic and smectic liquidcrystal materials (M. Kobayashi et al., IEEE J. Quantum Elect. OE-18,1603, 1982; T. G. Giallorenzi et al., J. Appl. Phys. 47, 1820, 1976; andS. S. Bawa et al., Appl. Phys. lett. 57, 1479, 1990). These devicesutilize refractive index changes due to molecular reorientation toprovide phase retardation. Some of these devices use prisms to couplemonochromatic incident light into a polymer waveguide, which in turn iscoupled into a liquid crystal waveguide. This technique is distinct fromprism coupling directly into the waveguide in that modulating the liquidcrystal waveguide refractive index does not affect the couplingcondition at the prism-polymer waveguide interface. Liquid crystals havealso been used in tunable Fabry-Perot filters (see, for example, M. W.Maeda et al. IEEE Photonics Tech. Lett. 2, 820 (1990) and A. Miller etal., U.S. Pat. No. 4,790,634) but, as in the case of liquid crystalwaveguides, they utilize molecular reorientation for modulation.

SUMMARY OF THE INVENTION

The present invention provides an electro-optic modulator, which, insome embodiments, utilizes the linear electro-optic effect in liquidcrystal materials. In the prior art, liquid crystal electro-opticmodulators operate by large molecular reorientation of the azimuthal ortilt angle of the molecular director in response to an applied electricfield. This leads to microsecond response times. In the presentinvention subnanosecond response times are provided by use of the linearelectro-optic effect.

The linear electro-optic effect results from the redistribution of boundcharges in a dielectric medium to produce a change Δn in the refractiveindex in response to an applied field E_(j) according to therelationship Δn_(i) αr_(ij) E_(j), where r_(ij) is the linearelectro-optic coefficient. In order to have a nonzero r_(ij), the mediumis required to have macroscopic order and noncentrosymmetric symmetry.This requirement is met by some liquid crystal materials, includingchiral smectic C* liquid crystals. Additional contributions to thedielectric response from rotation about the molecular long axis,reorientation about the short axis, and intramolecular rotation increasethe electro-optic coefficient of chiral smectic liquid crystals beyondthe effect of electronic oscillations alone.

In order to utilize the linear electro-optic effect in preference tochanges in the azimuthal or tilt angle, the modulators of the presentinvention provide a means for restricting change in the orientation ofthe molecular director. This can be accomplished by switching theapplied field E_(j) at a frequency greater than the response time forreorientation of the molecular director, or by applying a bias fieldE_(B) to fix the molecular director position.

One embodiment of the modulators of the present invention employs aFabry-Perot cavity to provide multiple optical passes through the liquidcrystal and thereby increase the interaction length with the light. Thisdevice comprises a liquid crystal cell with electrodes for applyingE_(j) and E_(B) placed between two partially or completely reflectivesurfaces. The Fabry-Perot resonance condition requires that an integralnumber of wavelengths be equal to the round trip optical path length ofthe cavity. As a modulator for monochromatic light, linear electro-opticswitching of the refractive index changes the cavity resonance conditionand thereby produces intensity modulations of the output beam. Whenutilized with a plurality of input wavelengths, the change in the cavityresonance condition changes which wavelength of light is output, thusproviding a tunable filter. In reflection mode it provides a phasemodulator.

Another embodiment of the present invention uses a waveguide to providemultiple passes through the liquid crystal material. This device iscomprised of cladding layers, with refractive indices less than that ofthe liquid crystal guiding layer, for confining light within thewaveguide, and electrodes for applying E_(j) and E_(B). Light can becoupled into and out of either the ends of the guide or the sides. Sidecoupling can be achieved by abutting prisms with refractive indicesgreater than the guiding layer index.

The function provided by the waveguide modulator of this inventiondepends on which coupling is employed and on whether the input light ismonochromatic or polychromatic. For end-coupling at both the input andoutput, the device of this invention provides phase and polarizationmodulation. When prism-coupling is employed at either the input or theoutput, or both, a coupling condition is imposed: the components of thewave vectors parallel to the gap must be equal in the prism and theguiding layer. Satisfying this coupling condition is dependent on thewavelength of light, the angle of the beam in the prism, the order ofthe waveguide mode, and the refractive index of the guiding layer.

For monochromatic light the waveguide modulators with side in, end-outcoupling and with side-in, side-out coupling are intensity modulators.The end-in, side-out device modulates the angle of the output beam,which, at a fixed point of observation, is equivalent to an intensitymodulation. An additional feature of the waveguide device is the abilityto select the thickness of the guiding layer to determine the number ofwaveguide modes for each wavelength. Thus a single input beam canproduce of number of simultaneously modulated output beams. When outputcoupling prisms are placed on both sides of the waveguide, output beamsare provided in both the reflected and the transmitted directions.

For polychromatic input light, the waveguide structure with at least oneprism coupling is a tunable filter. When polychromatic light isend-fired into the waveguide all the wavelengths enter the guidinglayer. At each wavelength the coupling condition at the output prism issatisfied at a different beam angle and thus the wavelengths arespatially dispersed. Tuning the refractive index of the guiding layertunes the output angles. From a fixed observation angle the device thusprovides tunable filtering of the polychromatic input light.

When polychromatic light is prism-coupled into the side of the waveguidetunable filter of this invention, the wavelength which satisfies thecoupling condition enters the guiding layer and the other wavelengthsare reflected. The guided wavelength can be output at the end or throughanother coupling prism. Tuning the refractive index of the guiding layertunes the wavelength which is coupled into the waveguide, thus providinga tunable filter.

The waveguide tunable filter with a prism-coupled input can be cascadedto provide simultaneous tuning and switching of multiple wavelengths.The wavelengths which are not coupled into each filter stage and whichare reflected at the waveguide interface are input into the next filterstage, wherein the refractive index of the guiding layer is tuned tocouple in one of these wavelengths and reflect the others. The cascadedfilters of this invention have particular utility in demultiplexingmultiple channels of optical communications systems.

The prism-coupled waveguide tunable filter of this invention can beimplemented with any electro-optic material, not limited to liquidcrystals, and with any electro-optic process, not limited to the linearelectro-optic effect.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows the dielectric constant of a chiral smectic liquid crystalas a function of modulation frequency.

FIG. 2 illustrates a liquid crystal linear electro-optic modulator.

FIG. 3A shows a liquid crystal linear electro-optic modulator within aFabry-Perot cavity. FIG. 3B shows the transmitted intensity as afunction of λ/n, and the effect of refractive index modulation onintensity.

FIG. 4A illustrates a liquid crystal linear electro-optic modulatorwithin a prism-coupled waveguide of order m. FIG. 4B depicts thetransmitted intensity of one of these orders at a fixed observationpoint as a function of sinΘ_(p) /n_(g), and the effect of refractiveindex modulation on intensity.

FIG. 5 shows the measured modulation in output intensity (bottom curve)with modulation of applied voltage (top curve) for a prism-coupledliquid crystal waveguide.

FIG. 6 shows the measured modulation depth of a prism-coupled liquidcrystal waveguide as a function of applied modulation field.

FIG. 7 illustrates a cascade of prism-coupled waveguide modulators withpolychromatic input light.

FIG. 8, comprised of FIGS. 8A-8H, shows a waveguide electro-opticmodulator with various combinations of end- and side-coupling and withmonochromatic or polychromatic input light.

DETAILED DESCRIPTION OF THE INVENTION

Conventionally, the electro-optic effects in chiral smectic liquidcrystals involve large molecular reorientation, which leads to nominallymicrosecond response time. This invention, however, focuses onelectro-optic modulation arising from excitations in the electronicstructure and molecular rotations that occur on the nanosecond or fastertime scale (≧GHz).

The linear electro-optic effect (Pockels effect) is so named because itrefers to a linear change in refractive index with applied electricfield, although it is, in fact, a second-order nonlinear X² process.Second harmonic generation, another X² process, has been previouslydemonstrated by the inventors (J. Y. Liu, Ph.D. Thesis) with the chiralsmectic liquid crystal BDH SCE9 (British Drug House). A nonlinearsusceptibility of d₂₃ =0.07 pm/V was obtained. The linear electro-opticcoefficients r_(ij) can be determined from the nonlinear susceptibilitytensor from the relationship ##EQU1## where n is the index ofrefraction. For liquid crystals n is approximately 1.5 so the expectedEO coefficient is r₃₂ =0.01 pm/V. Measurements with the modulator of thepresent invention, described in detail below, show that the electroopticcoefficient for BDH SCE9 is r₃₂ =3.6 pm/V, which is two orders ofmagnitude larger than the value expected from Eq. 1.

Second harmonic generation operates at optical frequencies and thereforeinvolves purely electronic oscillations. To explain the discrepancybetween r_(ij) and d_(ji), possible additional contributions to thedielectric constant within the GHZ operating frequency range of thelinear EO modulators of the present invention are considered.

The dielectric behavior of the liquid crystal materials has been widelystudied and recently different contributions to the dielectricpermittivity in CSLCs have been plotted. The results of the prior art(Gouda, op. cit. and Buka, op. cit.) are combined in FIG. 1 to show thefrequency dependence of the complex dielectric permittivity.

Referring to the drawings, like numbers represent like elements and thesame number appearing in more than one drawing represents the sameelement.

In FIG. 1 the dielectric constant 470 is shown as a function offrequency. Also shown are the modes contributing to the dielectricconstant 400-450 and the frequencies of optical absorption 460associated with these modes. The Goldstone mode 400, which refers tofluctuation of the azimuthal angle ψ, around the cone angle Θ, has arelaxation frequency in the range 10-500 Hz. The soft mode 410,connected to the tilt-angle fluctuation Θ, has a relaxation frequency inthe range 10³ -10⁶ Hz and is in general strongly temperature dependent.Molecular rotation about the short axis 420 has a relaxation frequencyof 10⁶ Hz. Molecular rotation about the long axis 430 and reorientationabout the short axis 435 have relaxation frequencies of 10⁹ Hz.Intramolecular rotation about a single bond 440 is at 10¹¹ Hz.Electronic oscillation 450 is the only contributor at higherfrequencies. Within the GHz operation frequency of the liquid crystallinear EO device of this invention, molecular rotation about the longaxis, reorientation about the short axis, and intramolecular rotationcan contribute to the dielectric response. These molecular motions arethe probable source of the increased linear EO effect beyond what ispredicted by the previous SHG measurements. Rotation of molecules withinan ordered medium is a motion unique to liquid crystals. This unexpectedtwo orders-of-magnitude increased response is a significant feature ofthe present invention.

In the linear EO effect, application of an electric field E_(j) changesthe refractive index via coefficients r_(ij). For chiral smecticC*liquid crystals, belonging to the point group C₂, in the presence ofan external field E_(y) the refractive index does not change in the ydirection. The induced refractive index change in the orthogonaldirections can be expressed by ##EQU2## This induced index of refractionchange, Δn, is typically small. For instance, if n=1.6, r_(ij) ≈1 pm/V,and E_(j) =10 V/μm, then Δn=2.0×10⁻⁵.

There are other smectic liquid crystal materials which are, in theabsence of an applied field, centrosymmetric and therefore notcandidates for the linear EO effect. In the device of this invention, abias field may be applied to materials such as SmA* and DHF to tilt themolecular directors and thereby break the centrosymmetry and make theelectro-optic coefficients nonzero.

The modulator of this invention utilizes the linear electro-optic effectin a liquid crystal cell to provide high speed modulation. The termliquid crystal cell is used herein to refer to transparent orsemi-transparent cells containing a liquid crystal material. Cells aretypically formed of uniformly-spaced transparent or semi-transparentretaining walls of an inert substrate, such as glass or quartz. Aconducting material is typically coated on the inside surface of thesubstrate walls to provide transparent, semi-transparent or reflectingelectrodes. Alternatively, the cells can employ lateral electrodes. Acomposition of liquid crystal materials is inserted between theuniformly-spaced electrodes and, for some materials, a method ofalignment of the liquid crystals is employed.

FIG. 2 shows the basic structure of the modulator of this invention,comprised of CSLC material 10, transparent or semi-transparentelectrodes 20, and modulation voltage V_(j) 22. In order to utilize thelinear electro-optic effect, the much larger changes in refractive indexdue to changes in the tilt and azimuthal angles must be suppressed. Thiscan be accomplished by modulating V_(j) at a frequency greater than theapproximately microsecond response time of molecular reorientation or byapplication of an optional bias voltage 24, V_(B) to pin the moleculardirector orientation. Electrodes 20 can be positioned as shown orlaterally to the liquid crystal layer to utilize particularelectro-optic coefficients.

The bias voltage can serve an additional function of enabling the use ofCSLC layers thicker than possible with surface stabilization techniques.In an ideal CSLC bookshelf geometry, where a high pretilt is introducedto the smectic layers, the directors remain everywhere parallel to thesubstrate surface, pointing along the z-axis when an electric field isapplied. However, in a CSLC cell with chevron defects, the smecticlayers bend inside the cell, and the CSLC molecules are no longeraligned uniformly. With an applied electric field, the spontaneouspolarization of the CSLC is forced to follow the field, and a moreuniform director distribution is achieved. Modulation of the chevronstructure can form another type of EO modulation.

In the preceding discussion three applications were identified for thebias voltage V_(B). The bias voltage functions by interacting with thepolar portion of the liquid crystal molecules and rotating the moleculardirector. This can be used to pin the molecules in one orientation sothat the modulation voltage V_(j) induces only the linear EO effect anddoes not tilt the molecules. This function can be performed without thebias voltage by modulating V_(j) at >MHZ frequency so that the moleculardirectors are, in effect, "pinned" by their slow response times. Thebias voltage can serve a second function of introducing a tilt to acentrosymmetric crystal and breaking the symmetry. Thirdly, it can beused to correct the alignment in defective crystal structures.Additional functions are described in the following description.

Input light 100 receives a phase shift travelling through the modulatorof FIG. 2. The phase shift in output light 110 is given by ##EQU3##where 1 is the optical path length, λ is the wavelength in vacuo, andk=2π/λ.

Two kinds of phase modulation methods are generally used to exploit thisphase shift. In the first one, birefringent phase retardation, themodulator of FIG. 2 is placed between two crossed polarizers. Typicallyincluded in the optical path is a birefringent crystal that introduces afixed retardation, so that the total retardation Φ is the sum of theretardation due to this crystal and the electrically induced one. Thetransmission through such a combination is modulated linearly by theapplied electric field.

The second method, Mach-Zehnder interferometry, refers the modulatedphase to the phase of an external interfering beam. This method requiresa source coherence over the interfering length. The incoming polarizedbeam is split in two by a beamsplitter, one of the two beams is phaseretarded by the modulator of FIG. 2, and the beams are recombined in asecond beamsplitter. The interference of these beams produces anintensity modulation.

The amplitude modulation depth of the above techniques is limited by theshort material interaction length. The embodiment of FIG. 3Aincorporates the liquid crystal into a Fabry-Perot resonator. Appliedvoltage 26 incorporates both the modulation voltage and the optionalbias voltage. Reflective surfaces 30 create a multipass cavity. Theeffective interaction length of the light beam with the CSLC is greatlyincreased by the multiple passes through the Fabry-Perot optical cavity.Thus, the modulation depth of the EO effect is enhanced.

In addition, the Fabry-Perot cavity imposes a resonance condition on theoutput beam 110 so that the device does not function as a pure phasemodulator. The round trip phase shift Φ of light passing through themedium is ##EQU4## The Fabry-Perot resonance condition requires that theround trip phase delay equal an integral number m of optical cycles

    Φ=m(2π),                                            (5)

for light to be transmitted. Using Eq. (4) for the phase delay in Eq.(5) gives as the Fabry-Perot resonance condition ##EQU5## Light whichdoes not satisfy this condition is reflected back toward the source.

Thus for polychromatic light, the transmission spectrum of the device ofFIG. 3A is a series of m peaks for the wavelengths which satisfy theresonance condition. FIG. 3B shows one of these transmission peaks 200.Tuning the refractive index with the application of field E_(j) tunesthe transmitted wavelengths. In this embodiment the modulator of thisinvention is a tunable filter. The tuning range is Δλ=(λ/n)Δn, where Δncan be obtained from Eq. 2.

When the incident light is monochromatic, the intensity of thetransmitted beam is a function of applied voltage V and is electricallycontrollable. FIG. 3B illustrates the modulation in output intensity 210with EO modulation of the refractive index 220. The Fabry-Perotresonator can be properly designed such that the transmission functionis at its steepest slope for the input wavelength in the absence of themodulation voltage, as illustrated in FIG. 3B. This can be achievedthrough appropriate choice of 1 or by using a bias voltage to tilt theliquid crystal molecules and select n.

The Fabry-Perot device can also be operated in reflection mode. In thisembodiment, one of the reflective surfaces 30 has R≈1 and the outputbeam overlaps the input beam. In the reflection mode configuration allwavelengths, resonant and otherwise, exit colinearly. Therefore, thedevice is a phase modulator enhanced by multiple passes, in contrastwith the amplitude modulator or tunable filter of the transmission modeembodiment.

Because of the sharp transmission function of the Fabry-Perot resonatorwhen provided with high finesse, the transmitted intensity is stronglymodulated with a relatively small modulating voltage. Using typicalvalues for n_(z) =1.65, l=5 μm, and R=0.9 and assuming r₃₂ =1 pm/V, themodulation depth obtained is ##EQU6## where the maximum refers to themodulation depth at the steepest slope of the transmission spectrum.This modulation depth is an order of magnitude greater than the singlepass phase-retardation embodiment of FIG. 2.

Multiple passes may also be achieved in a waveguide structure. In thisembodiment, the EO device of FIG. 2 is sandwiched between claddinglayers with lower refractive indices. The input light can be coupledinto and out of the ends of the waveguide or the sides. End coupling canbe performed, for example, with a focused beam or a fiber optic input.Side-coupling can be performed, for example, by gratings (T. Tamir inTopics in Appl. Phys. 7, Integrated Optics, edited by T. Tamir,Springer-Verlag, New York, 1979, p. 83) or by prisms (Tien, op. cit.).These side-coupling techniques are functionally equivalent and the prismis used for illustration. The prism-coupled waveguide embodiment of thepresent invention is shown in FIG. 4A. The guiding layer 10 is a liquidcrystal EO modulator with index n_(g). On at least two sides arecladding layers 40 of low refractive index material of index n_(c) wheren_(c) <n_(g). Electrodes 20 apply a voltage 26 which includes themodulating voltage V_(j) and can include the optional bias voltageV_(B). The electrodes can alternatively be placed in a lateraldirection. Prism 50 with index n_(p) >n_(g) abuts the thin-filmwaveguide. Prism 50 comprises coupling-in prism 52 with base angle Θ_(B)and coupling-out prism 54. A second prism 50 can be placed on theopposite side of the waveguide including coupling-out prism 56. Inputbeam 100 can be polarized by optional polarizing element 72 and focusedby optional focusing means 74. The output can be sensed, for example, bysensing element 76.

When the components of the wave vectors parallel to the gap are equalfor both the waves in the prism and in the film, the coupling reachesits peak and the light is efficiently coupled into the thin film. If thewave vectors are different, the net coupling is, in general, very small.The coupling is a function of input angle Θ_(p) and the refractiveindices of the waveguide layer and the prism. For propagation in thewaveguide, the summed round trip phase delay must equal an integralnumber m of cycles, 2mπ. The optical waveguide can support m modes, withphase velocities ν_(m). The waveguide propagation constant is β_(m)=ω/ν_(m) where ω is the angular frequency of the waveguide mode.Therefore the coupling condition is

    kn.sub.p sin θ.sub.p =Kn.sub.g sin θ.sub.g =β(8)

where Θ_(p) is the angle of the beam in the prism and Θ_(g) is the anglethe guided beam, both with respect to the substrate normal. When Eq. 8is satisfied coupling becomes effective, and optical energy can betransferred from the prism to the film and back from the film to theprism.

FIG. 4A shows the propagation of a waveguide mode 105. Two series ofm-lines, the "reflected" lines 112, and the "transmitted" lines 114, areoutput by the device of this embodiment. Each of the lines is due to awaveguide mode of a different order m. The order m is determined by thethickness of the waveguide.

With thick cladding layers, weak coupling (sharp mode profile) occursbetween the prism and the thin-film waveguide. This allows the modeequations to be expressed by the transcendental equation (Tien, op.cit.), ##EQU7## With the index of refraction of the guiding layer, n_(g)modulated by the electric field, we have

    n'.sub.g =n.sub.g ±Δn(E)                          (10)

where Δn(E) is the modulated index of refraction and is dependent uponthe applied electric field. Substitute Eq. 10 into Eq. 9, we have a modeequation modulated by the electric field.

The modulation of n_(g) in the z direction (perpendicular to theelectrodes) by the linear EO effect is given by n_(z) in Eq. 2.Substituting Eq. 2 into Eq. 9 gives the mode equation ##EQU8## Becausethe propagation constant β is related to the incident angle by Eq. 8, afluctuation of Δβ which is introduced by the perturbation of therefractive index will change the coupling angle of the prism module,ΔΘ_(p). Conversely, for a fixed angle of incidence Θ_(p), modulation ofn_(g) determines whether the beam will be coupled into the waveguide orreflected at the prism-waveguide interface. Thus, for monochromaticlight at a fixed angle of incidence the device of FIG. 4A is anintensity modulator.

FIG. 4B shows a waveguide mode intensity profile 300 as a function ofsin Θ_(p) /n_(g). The half-width of the waveguide mode is ΔΘ_(FPHW)(full power, half-width). Electro-optic tuning of n_(g) 320 modulatesthe output intensity 310. The amount of change, ΔΘ_(p), with respect toΔV is calculated with n_(p) =1.72309 (Scott SF10 glass at λ=0.6328 μm)and the base angle of the prism Θ_(B) =60°. Using typical values n_(g)=n_(CSLC) =1.65, poly-vinylalcohol (PVA) cladding layer with n_(c)=1.515, r₃₂ =1 pm/V, guiding layer thickness l=1.5 μm and cladding layerthickness S=1 μm gives ##EQU9## for the modulation depth, which is aboutone order of magnitude more sensitive than the Fabry-Perot electro-opticmodulator method.

In waveguides with increased cladding layer thickness, there is atrade-off between decreased coupling strength and sharper resonances. Inthe waveguide embodiment of this invention the cladding layer thicknesscan be smaller at the light input location for increased coupling andlarger in the guiding portion for better confinement.

FIG. 5 demonstrates intensity modulation by the prism-coupled waveguideembodiment of this invention. Two high index prisms were coated withindium-tin-oxide (ITO) transparent electrodes. A thin PVA layer whichacts as both an aligning layer and a cladding medium, was spun on top ofthe ITO. A BDH SCE9 layer was used for the guiding layer. Modulation ofthe applied voltage 330 at 6 kHz produced modulation of the outputintensity 310.

Using BDH SCE9, electro-optic frequency response has been measured up to20 MHz, the highest modulation speed achieved in CSLCs to date. Thelimitation is due to the complex impedance mismatch between the electricfield driver and the prism-waveguide cell. However, with impedancematched electrodes (e.g. transmission line electrodes) GHz modulationcan be achieved.

FIG. 6 shows the modulation depth of the CSLC waveguide modulator as afunction of applied field. The linear relationship demonstrates that themodulator utilizes linear electro-optic effect.

Another embodiment of this prism-waveguide module is a high speedoptical tunable filter. With a modulation of n_(g), the couplingcondition (Eq. 8) can be satisfied by a corresponding change in λ(recall k=2π/λ). Thus for polychromatic input light, the wavelengthwhich meets the coupling condition for a given n_(g) is coupled into theprism and other wavelengths are reflected. The tuning range of thisdevice is calculated from the derivative of Eq. 11 with respect to λ andn_(g) to give ##EQU10## When n_(c) -n_(p) is small, the tuning range isexpected to be very large, even with a small perturbation of the indexof refraction of the guiding material. For example, with λ=1.55 μm,n_(g) =1.65, n_(c) =1.5, n_(p) =1.65 and h=1.5 μm, the calculatedoptical tuning range is 220 nm for Δn_(g) =0.01.

The prism-coupled waveguide tunable filter of this invention can becascaded in series as shown in FIG. 7. In this and the following figure,the refraction of light at the prism-air interface is not depicted.Polychromatic light 100 is input into the first filter. The refractiveindex of the guiding layer is chosen to couple out light 112 and 114 ofwavelength λ₁ and reflect the other wavelengths 118 into a second stage,which selects a second wavelength. This provides simultaneousmultichannel operation without needing to divide the incident beam foreach channel. This cascaded filter embodiment can use any kind ofelectro-optic tuning method to choose n_(g) for each filter stage. Incombination with wavelength selection, the intensity of each channel canbe rapidly modulated by the linear electro-optic effect.

This invention provides several embodiments of the prism-coupledwaveguide modulator as shown in FIG. 8. They differ in the mechanism ofcoupling light in and out of the waveguide. The waveguide consists ofguiding layer 10, cladding layer 40, electrodes 20, and substrates 60 ofrefractive index n_(S). The devices with side couplers include prisms 52and 54. The substrate may also serve as a cladding layer in lieu of theseparate layer 40, in which case the refractive indices are in the ordern_(P) >n_(g) >n_(S), n_(c).

The device of FIG. 8A employs end coupling for both the input light 100and output light 110. With opto-electronic modulation of the refractiveindex, it functions as a phase and polarization modulator formonochromatic light or polychromatic light (FIG. 8E).

In the device of FIG. 8B the input light is prism-coupled 52 and theoutput is end coupled. As the refractive index of the guiding layer ismodulated, the light 100 is either reflected from the waveguide 118 orcoupled into the waveguide and transmitted out the end 116. The dottedlines 116 and 118 indicate that, depending on the refractive index ofthe guiding layer, one or the other of these beams is present. Thisdevice is therefore an intensity modulator and the light is switchedbetween two outputs. For polychromatic light (FIG. 8F), modulation ofthe refractive index changes the coupling condition and tunes whichwavelength is coupled into the waveguide and transmitted out the end 116and which is reflected 118. It is therefore a tunable transmissionfilter at beam 116 and a notch filter at beam 118.

When the output of the waveguide is prism-coupled 54 (FIG. 8C),modulating the index of refraction changes the angle at which thecoupling condition is satisfied. Input light 100 is output 112 throughthe prism at angle Θ_(P). This device can be used as a beam deflectoror, from a fixed observation angle, as an intensity modulator formonochromatic light. For polychromatic light (FIG. 8G), the output angleof each wavelength varies with the refractive index. From a fixedobservation angle this device is therefore a tunable filter.

In the device of FIG. 8D prism-couplers are employed at both the input52 and output 54. The input beam 100 is either reflected from thewaveguide 118 or coupled in and then coupled out again 112. Theintensity is modulated between the reflected and coupled beams withmodulation of the refractive index. For polychromatic light (FIG. 8H)the device modulates which wavelength is coupled in and whichwavelengths are reflected, thereby providing a tunable filter. A secondoutput coupling prism 56 can be placed on the opposite side of thewaveguide to provide beams in the transmission direction, as illustratedin FIG. 4A for monochromatic light and in FIG. 7 for polychromaticlight.

The liquid crystal modulators of the present invention can utilize thelinear electro-optic effect alone. They can also simultaneously utilizethe Goldstone or soft dielectric modes which produce refractive indexchanges via reorientation of the molecular director. These modes providea larger range of refractive index tuning but at a lower speed. Forexample, the amplitude modulator can utilize periodic changes in themolecular orientation as a carrier sub-frequency for the high speedlinear electro-optic modulation. As another example, the tunable filtercan use the molecular reorientation to select one of a plurality ofwavelengths and the linear EO effect to modulate the intensity of eachwavelength. In addition, CSLCs have been successfully oriented on manysubstrates, including GaAs and Si, which provides a potential fornumerous hybrid structures with other optical or electronic elements.

Liquid crystal materials have a number of advantages over othermaterials for use in the linear electro-optic waveguide modulator.Because their refractive indices are around 1.5, compared with muchhigher values for inorganic crystals, it is easier to fabricate claddinglayers with a similar refractive index. Poly-vinyl-alcohol,poly-butyl-thalate (PBT), Nylon, and SiO are examples of suitablematerials. Molecular tailoring of liquid crystals can be employed tomatch the index with the cladding layer. Molecular tailoring can alsoproduce molecules with increased nonlinear optical response.

The thickness of liquid crystal cells can be readily chosen to selectthe order of the waveguide. Depending on the application, the order ischosen to provide one output beam or multiple output beams. Single orderwaveguides can be fabricated with liquid crystals of about 1 μmthickness. Higher order waveguides require thicker cells. Because thelinear electro-optic effect does not necessarily involve motion of themolecular director, a large bias field can be used to force thealignment of the liquid crystal molecules, and cell thickness is notlimited by the requirement of surface-stabilized alignment.

If high output intensity is a requirement, a channel waveguide may beemployed instead of the planar waveguide illustrated. A channelwaveguide requires low index layers on all four sides of the guidingmedium. This can be elegantly implemented in CSLCs in planar cells byusing patterned electrodes to apply one voltage to a channel portion ofthe liquid crystal material and a second voltage on either side (J. Y.Liu, Ph.D. Thesis). This creates borders of lower index material oneither side of a center strip and thus defines the second pair of sidesof the waveguide channel. This CSLC waveguide structure can beelectronically controlled and, because there are no physical boundariesbetween the liquid crystal guiding and cladding layers, the scatteringis reduced.

This invention provides a modulator, as shown in FIGS. 2, 3, 4, 7, and8, utilizing the linear electro-optic effect in liquid crystals. Inaddition it provides a prism-coupled waveguide tunable filter embodimentof the modulator (FIG. 7 and FIG. 8F-H) used with any electro-opticmaterial and any electro-optic tuning process. The embodimentsillustrated here are examples of this invention but do not imposelimitations upon it. Other embodiments and applications will be readilyapparent to those skilled in the art.

We claim:
 1. An electro-optic modulator for modulating a characteristicof light, comprising a liquid crystal cell, said liquid crystal cellcomprising:a) liquid crystal material having a nonzero linearelectro-optic coefficient r_(ij), said liquid crystal materialcharacterized by a molecular director having a tilt angle and anazimuthal angle; b) means for applying an electric field E_(j) to saidliquid crystal material; and c) means for restricting change in the tiltangle and azimuthal angle of the molecular director of said liquidcrystal material in response to said electric field E_(j) ; d) whereinapplication of said electric field E_(j) changes the refractive index ofsaid liquid crystal material via the linear electro-optic effect.
 2. Themodulator of claim 1 wherein said means for restricting change in themolecular director comprises switching said electric field E_(j) at afrequency greater than the tilt angle and azimuthal angle response timesof said liquid crystal material.
 3. The modulator of claim 1 whereinsaid means for restricting change in the molecular director comprisesapplication of a bias field E_(B) to said liquid crystal material. 4.The modulator of claim 1 wherein said modulator further comprises aFabry-Perot cavity disposed about said liquid crystal material, saidFabry-Perot cavity comprising two reflective surfaces withreflectivities less than or equal to one.
 5. The modulator of claim 1wherein said modulator further includes a waveguide means for providingmultiple passes for light through said liquid crystal material, andmeans for coupling light into and means for coupling light out of saidwaveguide means.
 6. The modulator of claim 5 wherein said means forcoupling light into and said means for coupling light out of saidwaveguide means comprise end-coupling means.
 7. The modulator of claim 5wherein at least one of said means for coupling light is a side-couplingmeans.
 8. The modulator of claim 5 wherein said means for coupling lightinto and said means for coupling light out of said waveguide meanscomprise side-coupling prisms.
 9. The modulator of claim 8 wherein saidmeans for coupling light out of said waveguide means comprises twoside-coupling prisms positioned on opposite sides of said waveguidemeans.
 10. The modulator of claim 8 wherein said light is monochromaticand said characteristic of light is the output intensity at a fixedangle of observation.
 11. The modulator of claim 1 wherein said liquidcrystal material is a chiral smectic C* liquid crystal.
 12. Themodulator of claim 1 further including means for tilting said liquidcrystal material to provide said nonzero linear electro-opticcoefficients.
 13. The modulator of claim 1 further including means formodulating said tilt angle or said azimuthal angle.